足球异常运动与其实际应用的MATLAB模拟  

Simulation of abnormal football movement and its practical application with MATLAB

作　　者：蒋心怡 吕建锋 JIANG Xin-yi;LV Jian-feng(Department of Physics,Beijing Normal University,Beijing 100875,China)

机构地区：[1]北京师范大学物理学系

出　　处：《大学物理》2019年第11期41-47,共7页College Physics

摘　　要：模拟并研究了马格努斯效应对足球的运动轨迹和进球概率的影响.首先通过受力分析建立起飞行中足球的质心运动方程,利用MATLAB模拟得到弧线球的运动特点:相比于理想的抛物线轨迹,弧线球的轨迹是一条不共面且不对称的弧线.然后基于蒙特卡罗算法,分析了利用弧线球进球的出射速度分布情况,并进一步得到了本文所考虑区域的有无马格努斯效应作用时进球概率的分布及差值分布,发现这两种情况下进球概率的相对大小呈现以球门为中心的交替辐射带状分布.The influence of Magnus effect on football trajectory and goal probability is studied.Firstly,the dynamical equation of the mass-center of football is established by analyzing the force exerted on it,and through the simulation by MATLAB,its motion characteristics are presented,namely,its trajectory is not coplanar either symmetric compared with the ideal parabolic ones.Then,by using Monte Carlo simulation,the initial velocity distribution for scoring the goal is also obtained.Furthermore,we get the goal probability distribution and the difference distribution between the two cases whether there is Magnus effect in the region considered,it is found that the relative magnitude of the goal probability of these two cases presents the alternate radiation bands which centered on the goal.

关 键 词：马格努斯效应 弧线球 蒙特卡罗算法 MATLAB模拟 

分 类 号：O313.3[理学—一般力学与力学基础] O4-39[理学—力学]